Question 30 exam 2020

Hello,

I don't see how to obtain the expression for the excess cost function \(f(x) - f(x^*)\). My problem is that I have an additional term than in the solution, namely \(x^*H(x - x^*)\) obtained by replacing \(q = H x^*\).

Thank you for your help

Top comment

Hi,
I think you forgot to substract the value of \( f(x^*) \).
Replacing \( q = H x^* \) you get that \( f(x) = \frac{1}{2} x^\top H x - x^T H x^* \) and \( f(x^*) = - \frac{1}{2} {x^*}^\top H x^* \),
hence \( f(x) - f(x^*) = \frac{1}{2} (x - x^*)^\top H (x - x^*) \).
Hope this helps.
Scott

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